By a classical result of Jordan each finite subgroup of a complex linear group GL_n(C) has an abelian normal subgroup whose index is bounded by a constant depending only on n. It has been asked whether this remains true for finite subgroups of the diffeomorphism group Diff(M) of every compact manifold M; in the present paper, using the geometrization of 3-manifolds, we prove it for compact 3-manifolds M.
On Jordan type bounds for finite groups acting on compact 3-manifolds / Zimmermann, Bruno. - In: ARCHIV DER MATHEMATIK. - ISSN 0003-889X. - STAMPA. - 103/ 2014:(2014), pp. 195-200. [10.1007/s00013-014-0671-z]
On Jordan type bounds for finite groups acting on compact 3-manifolds
ZIMMERMANN, BRUNO
2014-01-01
Abstract
By a classical result of Jordan each finite subgroup of a complex linear group GL_n(C) has an abelian normal subgroup whose index is bounded by a constant depending only on n. It has been asked whether this remains true for finite subgroups of the diffeomorphism group Diff(M) of every compact manifold M; in the present paper, using the geometrization of 3-manifolds, we prove it for compact 3-manifolds M.File in questo prodotto:
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